Simple Mathematical Tool for Statistical Description of Dynamical Systems under Random Actions. I

摘要

In the lectures, the differentiation formulae (DF) for statistical averages is introduced in a compact form. The first part of these lectures is devoted to a general description of the DF method. The procedure of obtaining exact and closed equations for mean values and probability distributions of linear and nonlinear macroscopic systems driven by coloured noise is illustrated. As models of coloured random perturbations, both random jump processes (Kubo--Anderson and kongaroo processes) and diffusion processes (Ornstein--Uhlenbeck, Rayleigh and Pearson processes) are considered.